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Stochastic semiclassical equations for weakly inhomogeneous cosmologies
Campos, Antonio; Verdaguer Oms, Enric, 1950-
Universitat de Barcelona
Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path effective action is simply related to the Feynman-Vernon influence functional which describes the effect of the ``environment,'' the quantum field which is coarse grained here, on the ``system,'' the gravitational field which is the field of interest. This leads to identify the dissipation and noise kernels in the in-in effective action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian stochastic source which couples to the Weyl tensor of the spacetime metric is seen to modify the usual semiclassical equations which can be veiwed now as mean field equsations. As a simple application we derive the correlation functions of the stochastic metric fluctuations produced in a flat spacetime with small metric perturbations due to the quantum fluctuations of the matter field coupled to these perturbations.
2010-05-11
Gravitació
Pertorbació (Dinàmica quàntica)
Cosmologia
Equacions diferencials estocàstiques
Física estadística
Gravitation
Perturbation (Quantum dynamics)
Cosmology
Stochastic differential equations
Statistical physics
(c) The American Physical Society, 1996
Article
The American Physical Society
         

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